Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T20:15:09.842Z Has data issue: false hasContentIssue false
  • English
  • Français

A CHARACTERIZATION OF COMPOSITION OPERATORS ON ALGEBRAS OF ANALYTIC FUNCTIONS

Published online by Cambridge University Press:  28 July 2008

Daniel Carando
Daniel Carando
Affiliation:
Departamento de Matemática—Pab I, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina (dcarando@dm.uba.ar)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give a characterization of composition operators between algebras of analytic functions on a Banach space. We show (under fairly general conditions) that they are precisely the multiplicative operators that are transposes of operators of between the preduals of the algebras. The special cases of $H^\infty(U)$ and $H_{\mathrm{b}}(U)$ are considered. In these cases, the composition operators are those which are pointwise-to-pointwise continuous and/or $\tau_0$-to-$\tau_0$ continuous (where $\tau_0$ is the compact-open topology). We obtain Banach–Stone-type theorems for these algebras.

Keywords

Primary 46G2046E50Secondary 46J10composition operatorsholomorphic functionslinearization of functions
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 51 , Issue 2 , June 2008 , pp. 305 - 313
Copyright
Copyright © Edinburgh Mathematical Society 2008